I hope you are doing well! I am assuming you will be conducting this research in an academic setting. If the participants choose to disclose information on their depression (i.e., no forced responses) via the BDI in an academic setting like a university, it is not considered protected health information, as you and your university are not HIPAA-covered entities. Regular approval through an IRB/HSC and deidentification of the data should be enough to safely conduct this research without needing an NIH Certificate of Confidentiality. I would, however, reach out to your IRB/HSC to discuss the proper procedure moving forward.
As the Beck scale assesses clinical data about the clients/subjects responding to the items, even though voluntarily submitted, steps would seem to be needed to protect identities. Depending on your subject population, I would directly consult Hippa to discern these fine points. Best wishes for success.
So, after discussing with IRB consultant, we figured out that using BDI-II without collecting any identifiable information does not need NIH Certification of Confidentiality.